Correlates of Protection, Thresholds of Protection, and Immunobridging among Persons with SARS-CoV-2 Infection

Several studies have shown that neutralizing antibody levels correlate with immune protection from COVID-19 and have estimated the relationship between neutralizing antibodies and protection. However, results of these studies vary in terms of estimates of the level of neutralizing antibodies required for protection. By normalizing antibody titers, we found that study results converge on a consistent relationship between antibody levels and protection from COVID-19. This finding can be useful for planning future vaccine use, determining population immunity, and reducing the global effects of the COVID-19 pandemic

and thresholds of protection from symptomatic infection, especially when different assays were used to assess neutralizing antibody titers. This is a critical issue for the field to reconcile in order to move forward with a defined correlate of protection. Khoury et al. used a meta-analysis of Phase 1/2 and Phase 3 vaccine trials (vaccine comparison approach, main article Figure 1) and estimated that 50% vaccine efficacy was achieved with a neutralization titer of 54 IU/ml (in a live virus neutralization assay). More recently, two studies used data from subjects with 'breakthrough infection' after antibody responses were measured following two doses of mRNA 1273 (n= 36) or ChAdOx1 nCoV19 (n= 47) vaccination to model the protection curve (main article Figure 1, panels D-F). Across these studies both pseudovirus and live SARS-CoV-2 neutralization assays were used to measure neutralizing antibodies. Interestingly, the estimated curves using data from the same pseudoviral neutralization IC50 assay yielded similar 70% protective threshold of 4 IU/ml and 8 IU/ml, respectively (4,5) (Appendix Figure 3). However, Feng et al. used both a pseudovirus neutralization assay and a live SARS-CoV-2 neutralization assay, and showed that the latter yielded a 70% protective titer that was >4-fold higher than the pseudovirus assay (in international units) (4). Given the large variance in neutralizing antibody reports for notionally similar groups of vaccinated individuals when different assays are employed, even after conversion to IU, it is perhaps unsurprising that similar assays yield more similar results once converted to IU, but it would appear that the different assays contribute directly to different estimated titers required for the same level of protection (even within the same study using the same breakthrough infections).

Normalizing neutralization titers between studies.
To normalize neutralization titers between the vaccine comparison study (1), and the breakthrough infection studies (4)(5)(6) we assumed that the geometric mean neutralization titer (all references to "mean of neutralization titers" in this text refer to the geometric mean) of individuals vaccinated with a particular vaccine should be equivalent across studies. That is, where is a given neutralization titer or geometric mean neutralization titer reported in a study , � is the geometric mean neutralization titer of a vaccine reported in the study and � is the corresponding normalized neutralization titer or geometric mean neutralization titer, after normalization to the geometric mean vaccine titer for vaccine from study . It is important to note that the above normalization assumes that the mean neutralization titer in the Phase 1/2 studies of each of these vaccines (7-9) (used in the Khoury et al.) is approximately equivalent to the mean neutralization titer for the corresponding vaccine in the breakthrough-infection studies (4)(5)(6). Of note is that vaccination schedules were not equivalent for ChAdOx1 nCoV-19 vaccinees in the Phase 1/2 trial (4 week schedule) and the Feng et al.
study (a mixture of prime-boost schedules of between <6 week and >12 week), where dose spacing was altered from the intended schedule due to supply issues (10). The mixture of dosing schedules is likely to make the mean neutralization titers differ between the studies. We assessed the impact of this difference using data reported in the meta-analysis of these neutralization results from a large number of the Phase 3 trial participants (11). Performing a weighted average of the neutralization titers of the whole population from this meta-analysis (which resembles the cohort in the Feng et al. study) we found the mean neutralization titer was only 1.40-fold higher than the average of vaccinees with doses spaced by <6 weeks (11) (i.e. the <6 week spacing is comparable with the Phase 1/2 trial cohort dosing regimen [9]). This demonstrated that differences in dosing schedules will only have a minor impact on the overall normalization of the

Data on breakthrough infection
Data was requested from the authors of (4-6). Raw data were provided by the authors for (6). Data were unavailable for the other two studies, and therefore were extracted from the published work. Data were extracted using Adobe Illustrator (by saving figures in an SVG format and using a text editor to extract coordinates of datapoints from the vector graphic images contained in the publication) from Extended data Figure 2 in (4), and the WebPlotDigitizer online application (https://automeris.io/WebPlotDigitizer/) from figure S10 in (5). The neutralization titers of the uninfected vaccinated groups and the symptomatic breakthrough infections groups were extracted. Neutralization data on control and breakthrough infections from (6) were provided by the authors.

Calculating the unadjusted protection curve from breakthrough infection data to compare with the fitted models
In the three breakthrough infection studies reported (4-6), two groups of individuals are considered, vaccinated individuals with breakthrough infection and vaccinated individuals without breakthrough infection. Importantly, their uninfected status is not necessarily due to vaccine protection but in many cases will reflect simply that those individuals were not exposed where E is the vaccine efficacy. Therefore, 3. The probability of exposure is independent of neutralization titer, i.e.
( ∩ ) = ( ) ( ) Given the above, we are primarily concerned with calculating the probability that an individual becomes infected given that they are exposed and have a given neutralization titer ( ).
Denote an individual's risk of becoming infected given that they are exposed and have a neutralization titer ( ) as, ( | ∩ ), therefore: We note, using conditional probability, and noting that the probability an individual was exposed if they were infected is 1, i.e. ( ∩ ) = ( ): Combining equations 1 and 2 above, and using assumption 2, it follows that: Therefore, the probability that an individual who is exposed becomes infected, given that  (12) (Appendix Table 5). These unadjusted protection curves were normalized to the fold-ofconvalescence scale in the same way as described earlier, to generate main article Figure 3.
The confidence intervals of these unadjusted estimates of protection were determined by parametric bootstrapping of the neutralization titers. That is, we first fitted the (extracted or provided) neutralization data for individuals with breakthrough infection ("cases", assume number of individuals) and uninfected vaccinated individuals ("uninfected-vaccinated", assume number of individuals) with a normal distribution using censoring regression (1).
These fitted distributions of the neutralization titers for cases and uninfected-vaccinated from each study were then sampled randomly and times, respectively, and the resulting data were used to recalculate the unadjusted protection of individuals within each 2fold range of neutralization titers (as describe above). This was repeated 10,000 times for each study, and the 2.5 th and 97.5 th percentiles of the 10,000 estimates of the unadjusted protection were used to estimate the confidence intervals. Some iterations produced missing values for the vaccine efficacy estimate because by random sampling some ranges of neutralization titers had no uninfected-vaccinated individuals -in this case we did two things, we excluded the missing iterations from the calculation of the confidence intervals and we also set these missing values to an extreme estimate of 1 or 0 (i.e. 0% protection or 100% protection) and recalculated the 95% CIs. We then took the maximum of these two approaches as the Upper bound of the 95% CI, and the minimum of these two approaches as the Lower bound of the 95% CI.

Estimating the standard deviation of neutralization titers
For the Feng et al. study, raw neutralization titers could be precisely extracted and in this case censoring regression was used to fit a normal distribution to the log-transformed data to estimate the standard deviation of (log10) neutralization titers from both assays reported in that study (4). However, for the Gilbert et al. study, the raw data were not available and so the standard deviation of the neutralization titers were calculated from the confidence interval reported for the means in table 1 of (5). This was performed as follows: where, is the geometric mean titer of the uninfected vaccinated population, and are the lower and upper bounds of the 95% CI of the mean (log10) neutralization titer for the uninfected vaccinated population and SD1 and SD2 are two estimates of the SD from the lower and upper bounds of the 95% CI, respectively. Note that neutralization titers for 1005 uninfected individuals vaccinated with mRNA-1273 were reported in this study.
We found that the standard deviation of the neutralization titers were close (Appendix Table 3 (5) and (4), respectively. Fitting was performed using a standard least squares approach, to the natural log of the extracted values (extraction described above) (Appendix Figure 4 and Appendix Table 4).
where is the probability density function of a normal distribution with mean and standard deviation . Note that the log-transformed neutralization titers in Feng et al., and Gilbert et al. appear approximately normally distributed (Appendix Figure 5).
Using equation 5 and the estimated parameters in Appendix Table 3 and 4, we calculated the efficacy of other vaccines that would be predicted by the models in the Gilbert et al. and Feng et al. studies (Appendix Figure 1).

Estimating non-inferiority or superiority margins that will give high confidence of at least 80% efficacy for a candidate vaccine
It is useful for regulators to be able to define minimum criteria for vaccine developers to meet in order to define an effective new agent based on neutralizing antibodies. However, given assay variability it is not possible to define a particular neutralizing antibody titer that should be achieved by a new vaccine in order for it to have a certain vaccine efficacy. Instead, direct comparison of a new candidate vaccine against an existing comparator vaccine in a noninferiority or superiority trial will be a more robust approach.
Here we estimate what difference in geometric mean neutralization titers between a candidate vaccine and an existing vaccine is acceptable/necessary in order for there to be a high confidence the candidate vaccine has at least 80% efficacy. This analysis can also be adjusted to report superiority / non-inferiority margins for other efficacy thresholds.  Figure 2). Thus, for a given reference vaccine with a mean (log10) neutralization titer , and a given fold-change in the geometric mean neutralization titer of a new candidate vaccine compared with that reference vaccine (10 ), we compute the lower 95% confidence bound of the estimated vaccine efficacy for the new vaccine with, using the model reported by (1): where, is the log10 of the neutralization titer (on a fold of convalescence scale) of the reference vaccine, 50 is the (log10) neutralization titer estimated to give 50% VE, is the slope parameter relating neutralization and vaccine efficacy, and is the probability density function of a normal distribution representing the distribution in neutralization titers induced by a given vaccine mean (log10) neutralization titer of and standard deviation of (log10) neutralization titers of . To compute the lower 95% confidence bound from this model, we use parametric bootstrapping (as in [14]). Briefly, we estimate the vaccine efficacy using the above model 50,000 times, after sampling the model parameters at random from a normal distribution to capture the uncertainty in these parameters. The normal distributions used for randomly sampling the parameters are assumed to have means given by the parameter estimates and standard deviations given by the standard error (and covariance matrix for jointly distributed parameters) of the estimated parameters 50 , log ( ) and obtained during model fitting in the original study (1). Given that the mean neutralization titer of the reference vaccine ( ) also contains uncertainty, we similarly, draw this parameter randomly using the standard error in estimated in the original study (1) (horizontal confidence bands, in Appendix Figure 2). Of the 50,000 repeated estimates we then take the lower 5 th percentile of these bootstrapped predictions to estimate the one-tailed lower 95% confidence interval of candidate vaccine efficacy given the fixed change in neutralization titer (shaded region in Appendix Figure 2). We then find the change in neutralization titer of the novel agent compared to the existing comparator vaccine that will provide a lower bound on the vaccine efficacy confidence interval of 80% (Appendix Figure   2, Appendix Table 2). Thus, as long as a candidate vaccine is shown to have a fold change neutralization titer compared to the comparator vaccine that is no less than this margin in a noninferiority trial (or more than this margin in a superiority trial), then the vaccine efficacy of the candidate vaccine has a high confidence of being above 80%.

Estimating assay variability for predicting an individual's level of protection
The 29  vaccine has an efficacy with a lower 95% confidence interval of 80%. Similarly, the same approach predicts that a candidate vaccine should have a GMT at least 2.6-fold higher the level seen in ChAdOx1 nCoV-19 vaccinees in order that there is high confidence that the predicted efficacy of the candidate vaccine is above 80%. Note that these non-inferiority/superiority margins are computed independently for different reference vaccines and depends on the uncertainty in the model parameters, as well as the uncertainty in the actual position of the reference vaccines (based on the Phase 1/2 clinical trial data) on the fold-convalescence scale (i.e. the horizontal error bars of the reference has been included in the margins reported for each vaccine).